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J. Phys. Chem. C 2007, 111, 738-748
Molecular Dynamics Study of Gas-Liquid Aqueous Sodium Halide Interfaces. II. Analysis of Vibrational Sum Frequency Generation Spectra Tatsuya Ishiyama and Akihiro Morita* Department of Computational Molecular Science, Institute for Molecular Science, Myodaiji, Okazaki 444-8585, Japan ReceiVed: August 11, 2006; In Final Form: October 14, 2006
The vibrational sum frequency generation (SFG) spectra of gas-liquid interfaces of NaCl and NaI aqueous solutions are computed and analyzed by molecular dynamics (MD) simulations using a flexible and polarizable molecular model. The MD calculations have reproduced the experimental features of SFG spectra, including observed perturbation on the NaI spectra in contrast to little perturbation on NaCl. Analysis of the nonlinear susceptibility revealed that the intermolecular correlation has a significant contribution to the vibrationally resonant amplitude, which largely distorts the generally accepted relationship between the SFG intensity and orientation of individual molecules. In NaI solutions, modest enhancement of ssp intensity in the 3400 cm-1 region is thereby elucidated by this mechanism. Regarding the sps spectra, three spectral components are assigned and elucidated. Calculated remarkable enhancement in the 3400-3800 cm-1 region for NaI solutions is found to be sensitive to the electric double layer structure. It is also revealed that the sps intensity is augmented by the intermolecular water-water correlation effect.
1. Introduction Vibrational sum frequency generation (SFG) spectroscopy has become increasingly popular since it was first reported by Shen and co-workers in 1987.1 By making use of the second-order nonlinear optical process, SFG is intrinsically sensitive to interfaces when the adjacent bulk regions are isotropic such as ordinary liquid or gas. The surface sensitivity of this nonlinear spectroscopy is acute in a monolayer scale, and it is applicable to a wide range of interfaces where the inversion symmetry is broken. This technique is particularly suitable for investigating the structure of gas-liquid interfaces, whereas few other experimental techniques of comparable and ubiquitous use are available.2-6 It is virtually a unique vibrational spectroscopy for the gas-liquid interfaces under ambient conditions. The SFG spectra offer valuable information on molecular identity, local environment, and the orientational structure at the interfaces. Although the observed SFG spectra involve rich molecular information on the interfaces, it is often a challenging issue to fully extract the information in a detailed molecular level. Experimental spectra are usually analyzed through decomposing them with certain Lorentzian functions or their analogues, but the fitting procedure of decomposition may not be unique when the spectra are complicated by overlap or interference of vibrational bands, extensive inhomogeneous broadening sensitive to local environment, etc. Each spectral component thus obtained is often difficult to be assigned, particularly when the spectral component of SFG does not obviously correspond to the infrared or Raman spectra. Although vibrational SFG spectroscopy has many similarities with infrared or Raman spectroscopies, the spectral features are not necessarily common due to the difference in optical processes and difference in surface and bulk environments. Another important issue in the * To whom correspondence should be addressed. E-mail: amorita@ ims.ac.jp. Also at Graduate University for Advanced Studies, Myodaiji, Okazaki 444-8585, Japan.
empirical analysis is the interpretation of the SFG amplitude in terms of the orientational structure and number density of interface species. Recently, much new experimental progress has been made to interpret the spectra. One of the remarkable attempts was reported by Wang and co-workers, who made thorough use of the light polarization combinations to analyze the orientational structure of surface molecules.7,8 They argue from their experimental analysis that the molecular orientation at the air-water interface is well ordered, which poses an interesting discrepancy with recent molecular dynamics simulations.9,10 Another promising attempt is the phase-sensitive measurement by Shen and co-workers, which experimentally reveals the phase information on the nonlinear susceptibility.11 In order to extract the molecular information from the SFG spectra, theoretical studies on SFG spectroscopy12-15 have also made considerable progress. The molecular dynamics (MD) simulation provides detailed structural and dynamical information on the interfaces within the accuracy of the molecular model. We have developed two theoretical formalisms to compute SFG spectra by ab initio molecular modeling and MD simulation, that is, the energy representation12 and the time correlation function representation.13 The power of the computational approaches is to allow us to analyze experimental SFG spectra directly in comparison with the interface structure that MD simulation can provide, though the computational cost is demanding. These first-principles approaches can greatly reduce the ambiguities associated with the empirical SFG analyses to help establish the relation between experimentally observed signals and interface structure. In this paper, we apply the MD analysis of SFG spectra to the gas-liquid interfaces of electrolyte aqueous solutions, which pose controversial problems, as discussed in the following. The molecular-level structure of gas-liquid interfaces of electrolyte aqueous solutions has been drawing renewed interest for the past decade.16-19 For more than a half century, most inorganic ions have been thought to be less stable at the vapor-
10.1021/jp065192k CCC: $37.00 © 2007 American Chemical Society Published on Web 12/10/2006
Analysis of Vibrational SFG Spectra water interface than in bulk water, presumably because the interface could provide an incomplete environment of solvation for the ions. This common notion has been justified experimentally by the concentration dependence of surface tension measurements20 and theoretically by the dielectric model of image force.21 In recent years, however, several MD results have been reported which appear contrary to the above conventional picture.19,22-28 Jungwirth and Tobias performed MD simulations of sodium halide aqueous solutions with a point dipole force field model and demonstrated that the surface concentrations of large, highly polarizable halide anions such as Br- and Iprefer the interface like a surfactant species.19,22,23 This MD result was confirmed by other polarizable force field models.24,25 The free energy calculations by Dang and Chang also supported the surface preference of bromide and iodide anions.26-28 These novel results are qualitatively explained by the fact that highly polarizable ions at the interface gain extra stabilization via polarization by the anisotropic electric field. It is also pointed out that the large size of ions is another important factor for driving them to the interface.29 To examine the controversial structure of the gas-liquid interfaces, SFG spectroscopy should have sufficient depth resolution at the interfaces. SFG is able to probe the structure of interfacial water possibly perturbed by the surface ions. The perturbation on the water orientational structure is shown to be conspicuous when the electric double layer is formed as a consequence of the surface segregation of anions.25 Therefore, the SFG spectra can shed light on the formation and influences of the electric double layer in a monolayer scale. It yields complementary insights into the interface structure to other experimental attempts trying to probe ions by surface-sensitive techniques.30-32 In fact, SFG studies on the effects of electrolytes on the gas-liquid interfaces of aqueous solutions have been extensively performed by Shultz and co-workers.3 Recently, the SFG experiments of sodium halide aqueous solutions were reported by different groups in connection to the above problem.33,34 Although the reported SFG spectra themselves largely coincide with each other, their interpretations remain controversial. Raymond and Richmond employed systematic H-D isotropic dilution to facilitate the decomposition analysis of the observed SFG spectra,35 and thereby elucidated the details of the hydrogen bonding network of interfacial water.33 They concluded that the water structure at the topmost layer is hardly perturbed by the ions, suggesting that the significant enhancement in anion concentration at the topmost layer is not present, even if anions come close to the interfacial region. On the other hand, Liu et al. discussed the perturbation of SFG intensity in comparison with those of infrared and Raman for the bulk liquid and concluded that the surface depth is increased in the aqueous solutions, essentially consistent with the prediction by the MD calculation.6,34 Judging from the above interpretations, it may be difficult to obtain a coherent picture about the surface structure from the empirical SFG analyses at the present stage. Therefore, reliable theoretical support is strongly required to solve these problems.17,36 In this paper, we performed SFG analysis of NaCl and NaI aqueous solutions using the time correlation formalism. Some preliminary results about the NaI solution at 2.1 M were presented in a previous letter, which demonstrated a significant intermolecular vibrational coupling effect in the SFG spectrum.37 This effect turned out to have a remarkable influence on the general relationship between the SFG intensity and orientational order in this system. The present paper expands the discussion and provides a more comprehensive analysis of the electrolyte
J. Phys. Chem. C, Vol. 111, No. 2, 2007 739 solutions, including the dependence of concentration and anion species. Furthermore, we deal with the SFG spectra of different polarization combinations, that is, ssp and sps, which provide complementary insight into the interface structure. Here, ssp (sps) denotes the polarization combination of s (s) for SFG, s (p) for visible, and p (s) for infrared, respectively, where p denotes the polarization of the electric field parallel to the incident plane and s the polarization perpendicular to it. The present SFG analysis is based on the molecular model we have developed in the preceding paper,25 and we refer to the investigation of the interface structure presented there.25 The remainder of this paper is constructed as follows. In the next section, we present the theory and computational procedures of SFG calculations by MD simulation. Then, the ssp and sps polarized SFG spectra of the electrolyte aqueous solutions are theoretically analyzed in sections 3 and 4, respectively. Section 5 is devoted to conclusions. 2. Theory and Computation of SFG Spectra The theoretical methods of computing the SFG spectroscopy are given elsewhere in detail,13,38 and accordingly, a brief summary is given here. 2.1. Expressions of Nonlinear Susceptibility. The SFG intensity, ISFG, is proportional to the square of the frequency-dependent second-order nonlinear susceptibility, χ(ωSFG, ωvis, ωIR),
ISFG ∝ |eSFG‚χ(ωSFG, ωvis, ωIR):eviseIR|2
(1)
where ωvis and ωIR are the frequencies of visible and infrared fields and ωSFG ) ωvis + ωIR is the sum frequency. eSFG, evis, and eIR denote the directions of the external electric fields of SFG, visible, and infrared, respectively. We note that χ in eq 1 represents the response to the external electric fields. The spectral shapes of the ssp and sps polarized intensity can be calculated via3,4
Issp
SFG
2 ∝ |χiiz|2, ISFG sps ∝ |χizi|
(2)
where the subscript i stands for x or y in the laboratory fixed coordinates. Here, z is normal to the gas-liquid interface, and the lateral directions of x and y are equivalent in the cylindrical symmetry. The nonlinear susceptibility, χ, is composed of the vibrationally resonant part, χR, and the nonresonant part, χNR,
χ ) χR + χNR
(3)
In the cases that the visible and SFG frequencies are off resonant, χR can be expressed as the Fourier-Laplace transformation of the time correlation function between the system dipole, M, and the polarizability, A,
χRpqr )
∫0∞dt eiω
i p
〈Apq(t) Mr(0)〉
IRt
(4)
To obtain the classical analogue of eq 4, the condition of detailed balance and zero point vibrations should be considered in the time correlation function,14 and the equivalent classical expression is given as38
χRpqr )
iωIR 2kBT
∫0∞dt eiω
〈Apq(t) Mr(0)〉cl
IRt
(5)
where kB and T are the Boltzmann constant and temperature and the expression 〈 〉cl indicates the statistical average in the
740 J. Phys. Chem. C, Vol. 111, No. 2, 2007
Ishiyama and Morita
classical mechanics. In the classical MD simulation, χR is calculated by eq 5, where the procedures to calculate A and M are presented in the preceding paper.25 2.2. Decomposition of Time Correlation Function. Once we calculate the nonlinear susceptibility as discussed above, we can theoretically analyze the mechanism of the time correlation function which constitutes the nonlinear susceptibility to get molecular sights into the SFG signals. In the following, we present two decomposition analyses of the time correlation function in eq 4 or 5. These analyses will be utilized later in sections 3 and 4. The system dipole moment and polarizability at time t, M(t) and A(t), are determined for an instantaneous configuration so as to satisfy the self-consistency in polarization. The results of self-consistent dipole and polarizability are composed as follows: 13,25
N
∑i
M(t) )
N
pi(t), A(t) )
∑i reffi (t)
(6)
where pi(t) is the dipole moment of the ith molecule at time t and reff i (t) is the effective polarizability including the local field correction. Therefore, the macroscopic susceptibility, χR, can be decomposed into the self-correlation part, χR(self), and the intermolecular correlation part, χR(corr),37
χRpqr )
N
i
N
∞ dt eiω t 〈(∑Reff ∫ pq (t))(∑pr(0))〉 0 p i j IR
) χRpqr(self) + χRpqr(corr)
(7)
where
χRpqr(self) )
i
N
∑∫ dt eiω p i 0 ∞
IRt
eff 〈Ri,pq (t) pi,r(0)〉
(8a)
N
≡ χRpqr(corr) )
R,eff ) N〈βR,eff ∑i βi,pqr pqr 〉
i
N
N
∑ ∑ ∫0 dt eiω p i ∞
IRt
(8b) eff 〈Ri,pq (t) pj,r(0)〉
(9)
j(*i)
R,eff In eq 8b, βi,pqr is the vibrationally resonant part of the effective hyperpolarizability of the ith individual molecule.37 The expression of χ in eq 8b, χ ∼ N〈β〉, is consistent with the common assumption in experimental analyses that the susceptibility, χ, is proportional to the number density, N, and the average molecular orientational order of individual molecules, 〈β〉.39 Equation 7 indicates that the common notion of χ ∼ N〈β〉 presumes that the self part governs the entire susceptibility. The validity of this assumption will be examined through directly performing the decomposition of eq 7 by the MD calculations. Another decomposition scheme of χR is carried out into molecular species. In the electrolyte aqueous solutions, the following decomposition into water, W, and ions, I (cations + anions), is performed:37
R,WW R,IW R,II + χR,WI χRpqr ) χpqr pqr + χpqr + χpqr
χR,mn pqr )
∫0∞dt eiω
i p
n 〈Am pq(0) Mr (t)〉
IRt
(10a) (10b)
where Am and Mm denote, respectively, the sum of effective polarizability and dipole of species m () W or I) species m
M (t) ) m
species m
∑i
pi(t), A (t) ) m
∑i
reff i (t)
(11)
Although the vibrational SFG spectra of the electrolyte aqueous solutions in 3000-4000 cm-1 are qualitatively attributed to the O-H vibrations of water, the SFG intensity could include significant contributions from other species. The decomposition of eq 10 allows for further insight in the correlation mechanism. Finally, we note that the above decompositions are represented on the basis of the quantum time correlation function of eq 4, though the decomposition schemes are the same using the classical expression of eq 5 except for the difference in the prefactor. 2.3. MD Computation. Technical details of the MD simulation are described in the preceding paper,25 and thus, a brief summary is presented in this subsection. The molecular model of water allows explicit electronic polarization and internal vibration. The electronic polarization is incorporated to deal with optical response, and the internal vibration for use of the time correlation function in the infrared frequency region. The present polarizable and flexible model is developed to represent the bulk and interface properties of aqueous systems, including the spectroscopic properties of O-H vibrations. The electronic polarizability is also incorporated in the models of ions.40-42 The performances of these molecular models were thoroughly examined in the preceding paper.25 The MD simulations are performed for an infinite slab geometry of aqueous solutions under the three-dimensional periodic boundary conditions. The long-range electrostatic forces of point charges and dipoles are treated by the Ewald summation. The unit cell is rectangular with dimensions of Lx × Ly × Lz ) 30 Å × 30 Å × 150 Å, where the z axis is normal to the gas-liquid interface. Each cell contains 1000 water molecules and an additional 20 (40) anions and 20 (40) cations for the 1.1 M (2.1 M) salt solution. The slab of aqueous solution has two sides of gas-liquid interfaces, which are sampled independently in the calculation of nonlinear susceptibility. MD trajectories were generated in the microcanonical ensemble with an average temperature of 298 K. In the calculation of the time correlation function 〈A(t)M〉, the statistical convergence is hindered by the noise from the bulk region. This problem is worse for a larger system size, as the volume ratio of the surface region to the bulk becomes smaller. To reduce the bulk noise, a filtering function, g(zˆ), is introduced:
g(zˆ) )
{
( )
tanh 0
zˆ - zˆr (zˆ > zˆr) w (zˆ < zˆr)
(12)
where zˆ ) |z - zGibbs| is a local z coordinate defined for each interface side of the slab, whose origin is located at the Gibbs dividing surface of water, (zGibbs. In this definition of zˆ, the region of zˆ > 0 means the vapor side from the Gibbs surface, while zˆ < 0 means the bulk liquid side. w denotes a tapering width, which was set to 1.0 Bohr (∼0.53 Å)38 in the present study. The system dipole and polarizability in eq 6 are practically calculated using the filtering function, g(zˆ), as
M)
∑i pig(zˆi),
A)
∑i reffi g(zˆi)
(13)
Analysis of Vibrational SFG Spectra
J. Phys. Chem. C, Vol. 111, No. 2, 2007 741
where zˆi is the local zˆ coordinate of the ith molecule and the summations of i are taken for each interface side. The filtering function is used to cut off the noise from the bulk region deeper than the zˆr plane. In the present calculation of SFG spectra, we set zˆr ) -10 Å as a default value, which has been confirmed to be a reasonable choice to facilitate the convergence of χ and not to distort the spectra. This choice is in accord with the fact that the density and orientational orders are randomized there in the MD calculations.25 The filtering function in eq 13 is of another use for spatial decomposition of χ. By calculating spectral change by eq 13 with systematically varying zˆr, we can discuss the spatial origin of the SFG signals, as discussed in section 4. The MD trajectories were produced in parallel with a total of 30 ns for each concentration and solute species. Consequently, the total statistical sampling for the calculation of χ amounts to 2 × 2 × 2 × 30 ) 240 ns for each system. The sampling number is doubled, respectively, by the two interface sides of the slab, equivalence of the x and y axes (χxxz and χyyz for ssp, χxzx and χyzy for sps), and equivalence of 〈A(t)M〉cl and 〈AM(t)〉cl in the classical time correlation functions. 3. Mechanisms of ssp Spectra This section deals with the ssp polarized SFG spectra, the most common polarization combination applied to the gasliquid interfaces. The computed SFG spectra and their dependence on solute species and concentration are compared with the experiments. Then, the nonlinear susceptibility is further analyzed by the two decomposition analyses of the time correlation function presented in section 2.2. SFG Spectra. Figures 1 and 2 display the results of ssp polarized SFG spectra calculated by eqs 2, 3, and 5 of pure water and NaCl and NaI aqueous solutions of 1.1 and 2.1 M concentrations, where a common nonresonant amplitude, χNR iiz , was empirically assumed as discussed below. These results are compared with the experimental ssp spectra by Liu et al.34 in panel b of Figures 1 and 2. The calculated ssp spectra of water and the aqueous solutions commonly reproduced the two-band structure, consisting of a sharp band at about 3700 cm-1 and a broad one in the 3000-3600 cm-1 region. The former band is assigned to the surface O-H stretching vibrations of dangling OH moieties in the hydrogen bond network, while the latter, to those of the hydrogen bonding OH.43 Regarding the dependence of solute species, noticeable differences in the ssp spectra are apparent between NaCl (Figure 1) and NaI (Figure 2). For NaCl solutions in Figure 1b, the NaCl solute has little influence on the experimental spectra over the 0-0.036x (x ) mole fraction of salt) concentration range. For NaI aqueous solutions, on the other hand, Figure 2b shows that the intensity at about 3400 cm-1 is somewhat enhanced with the NaI concentration, implying some structural changes at the interface, while the intensity of the 3700 cm-1 band is less perturbed by the ions. These essential features of NaCl and NaI solutions are reproduced in the calculated spectra in Figures 1a and 2a, respectively. Previous MD calculation by Brown et al.36 also reported the enhanced SFG signal at about the 3400 cm-1 region for the 1.2 M NaI aqueous solution, though the magnitude of enhancement was strongly overestimated presumably due to their simplified force field (a flexible and nonpolarizable water model) or the sampling problem. The next question is how the observed/calculated SFG spectra of the aqueous solutions are interpreted in terms of their interface structures, which were investigated in detail by molecular dynamics in the preceding paper.25 The density profile at the
Figure 1. SFG spectra of ssp polarization for NaCl solutions and pure water obtained by (a) MD calculations and (b) experiments. (Panel b is reproduced from ref 34 with permission. Copyright 2004 American Chemical Society.)
interfaces (see panel a of Figure 11) indicates that neither Na+ nor Cl- ions preferentially come to the gas-liquid interface in the NaCl solutions, while I- anions are segregated to the interface to form an electric double layer in the NaI solutions. The electric double layer in turn remarkably induces the orientational order of water molecules. It was pointed out in previous studies that the induced orientational order of water molecules is largely responsible for the enhancement of SFG spectra.3 However, according to the conventional view that the orientational order largely governs the SFG intensity, the spectral change for NaI solution, particularly the 1.1 M case, seems to be quite modest in spite of the drastic change in the water orientational order, as discussed in section 4.2 of the preceding paper.25 Our preliminary report37 addressed this question and elucidated the fact that the intermolecular vibrational correlation plays a substantial role in the spectral changes at about 3400 cm-1, besides the orientational order of water. In the present paper, we expand the discussion and demonstrate that the vibrational coupling effect is indispensable for quantitative interpretation of the SFG spectra. Nonresonant Susceptibility. In the following, we deal with the nonlinear susceptibility, χiiz, that includes amplitude and phase. Before discussing its vibrational structure, we make some comments on the nonresonant term, χNR iiz , which is treated empirically as a fixed parameter. The optimized nonresonant term is real and negative, and its amplitude, -χNR iiz , is expressed with the dashed horizontal lines in panel a of Figures 3 and 4. Note that the dashed lines correspond to the shifted zero level for the total real amplitude Re[χiiz] ) Re[χRiiz] - (χNR iiz ). The nonresonant amplitude is necessarily negative to
742 J. Phys. Chem. C, Vol. 111, No. 2, 2007
Figure 2. ssp SFG spectra for NaI solutions and water obtained by (a) MD calculations and (b) experiments.34 (Copyright 2004 American Chemical Society.)
reproduce the spectral dip at about 3600 cm-1 observed in the experimental SFG spectra, as shown in Figures 1 and 2. We assumed a common amplitude for all of the systems (χNR iiz ) -0.7 arb units in Figures 3 and 4) so as to reproduce the lowfrequency tail of the experimental ssp spectra at about 3000 cm-1, where the vibrationally resonant amplitude is relatively minor in the SFG intensity. This assumption does not appear to be in accord with the experimental suggestion by the H-D substitution33 that the NaI solution has an enhanced nonresonant amplitude as compared with that of the pure water by a factor of ∼1.5. We think this problem should be further pursued to solve this apparent inconsistency, via analyzing the physical meaning of the phenomenological “nonresonant” amplitude for the D-substituted analogues. Self- and Intermolecular Correlations. Next, we focus on the vibrational resonant term, χRiiz, and perform the decomposition analysis into the self part, χRiiz(self), and correlation part, χRiiz(corr), by eq 7. Figures 3 and 4 show real and imaginary parts of χRiiz for water and the aqueous solutions, while the insets display those of χRiiz(self). Note that the difference of χRiiz and χRiiz(self) corresponds to the correlation part, χRiiz(corr), though not explicitly displayed. In the case of NaCl solutions in Figure 3, the χRiiz values of both 1.1 and 2.1 M solutions are quite similar to that of pure water. This similarity in χRiiz is consistent with the surface structure (density and orientation) of water by MD simulation,25 which is little perturbed by the dissolution of Na + and Cl-.
Ishiyama and Morita
Figure 3. (a) Real and (b) imaginary parts of the iiz (i ) x, y) nonlinear susceptibility, χRiiz, for NaCl solutions and pure water. The insets show the self part, χRiiz(self), in the same scale (see eq 8a). The dashed horizontal line in panel a indicates -χNR iiz . (This line corresponds to the shifted zero level for Re[χ] ) Re[χR] + χNR.)
Comparing the main panels with those of the insets, we find that the spectral shape of each χRiiz resembles that of χRiiz(self), implying that the SFG spectra of NaCl solutions can be interpreted with the self part of correlation, at least qualitatively, that consists of the individual molecular responses. This is rather in accord with the conventional picture of the nonlinear susceptibility, χ ∼ N〈β〉, as discussed in section 2.2. In the case of NaI solutions in Figure 4, on the other hand, the spectral shapes of χRiiz are remarkably different from those of the self part, χRiiz(self), as shown in the insets. Consequently, the self part, χRiiz(self), of NaI solutions is also distinct from that of pure water, although the χRiiz term itself shows less pronounced differences between the NaI solutions and pure water. In particular, the sign of the imaginary self part, Im[χRiiz(self)], is negative for pure water but positive for the NaI solutions in the hydrogen bonding frequency region, 3000-3600 cm-1. The concentration dependence of NaI solutions (1.1 and 2.1 M) is also more apparent in the self part, χRiiz(self), than χRiiz, as Figure 4 shows that the amplitude of Im[χRiiz(self)] is clearly enhanced as the concentration of NaI increases. These drastic behaviors in the self part are in fact more amenable to the straightforward interpretation with the orientation of surface water.12 The difference in Im[χRiiz(self)] implies that the water molecules in a pure water surface direct their dipoles toward the liquid phase, whereas the dipoles in NaI solution surfaces are reversed, which is totally consistent with the results of the MD investigation.25 We remind the reader that this intuitive interpretation in terms of the individual molecular orientation is justified
Analysis of Vibrational SFG Spectra
J. Phys. Chem. C, Vol. 111, No. 2, 2007 743 mechanism is more conspicuous for NaI solutions than NaCl solutions. This intermolecular (water-ion) dipolar correlation significantly suppresses the net amplitude of χRiiz. The mechanism of the out-of-phase vibrational correlation is schematically illustrated in Figure 6a. The dipole-dipole interaction tends to induce surrounding dipole moment in phase along the vertical direction while out of phase along the lateral direction. Accordingly, when an ion located at the interface has an induced dipole moment along z, as shown in Figure 6a, the induced dipoles of the surrounding water should have a net outof-phase component due to the inhomogeneous environment of the gas-liquid interface. This vibrational correlation mechanism is emphasized in a strongly interacting system including highly polarizable anions. The above analysis revealed that the ssp polarized SFG spectra of the electrolyte solutions are relatively insensitive to the formation of the strong electric double layer structure due to the “canceling mechanism” by the water-ion dipolar correlation. 4. Mechanisms of sps Spectra
Figure 4. (a) Real and (b) imaginary parts of χRiiz for NaI solutions and water. The insets show the self part, χRiiz(self). The dashed horizontal line in panel a indicates -χNR iiz .
for the self part, χR(self), by eq 8b. However, the above features in the self part are less obvious in χRiiz, and accordingly, the intuitive interpretation of molecular orientation is not as valid for χRiiz as for χRiiz(self) in the NaI solutions. The salient difference between χRiiz and χRiiz(self) demonstrates a significant contribution of the intermolecular correlation part, χRiiz(corr), in the nonlinear susceptibility, χRiiz. Water-Ion Coupling. The origin of intermolecular correlation is further elucidated via decomposition of χR by molecular species, as discussed in eq 10, into the following four terms:
{
χR,WW χR,WI χR,IW χR,II
water polarizability - water dipole water polarizability - ion dipole ion polarizability - water dipole ion polarizability - ion dipole
(blue) (red) (green) (pink) (14)
Figure 5 shows the imaginary part of the four components, χR,mn iiz , of varying concentration and solute. In all of the panels, (green lines) and χR,II χR,IW iiz iiz (pink lines) are negligible in comparison with other components, since ions have little vibrational components of polarizability.37 A marked feature in ] Figure 5 is that, as the ion concentration increases, Im[χR,WW iiz (blue lines) positively increases in the 3000-3600 cm-1 region, whereas Im[χR,WI iiz ] (red lines) negatively increases so as to cancel out the former amplitude. The opposite signs of Im[χR,WW ] (blue lines) and Im[χR,WI iiz iiz ] (red lines) indicate that the water dipoles and ion dipoles along the z direction are oscillating out of phase with one another. This cancellation
The sps combination of polarization provides useful complementary information to the ssp combination on the interface structure, though the sps spectra have been less explored for the SFG studies on the liquid interfaces. This is partly because intuitive interpretation of the sps spectra may be less obvious than ssp. The sps spectra involve Aiz and Mi terms in the time correlation function of eq 4 or 5, and the average of each term vanishes at the interface, 〈Aiz〉 ) 0 and 〈Mi〉 ) 0 for sps. This is in contrast to the ssp case that 〈Aii〉 * 0 and 〈Mz〉 * 0 at the interface. Consequently, the correlation of Aiz and Mi is essential to understand the sign (phase) of the sps susceptibility, whereas the Mz term is usually thought to govern the behavior of χiiz in the ssp case. In this section, we first display the calculated sps spectra and then analyze the mechanism of the nonlinear susceptibility. The MD simulation is shown to be also useful to shed light on the mechanisms of sps spectra, as discussed in the following. Calculated sps Spectra. Figure 7 shows the calculated SFG spectra of the sps combination for pure water and NaCl and NaI solutions of 1.1 and 2.1 M concentrations. Our simulation well reproduces the overall features of the experimental sps spectra of salt solutions;44 that is, (i) the spectra have two broad peaks at about 3500 and 3700 cm-1, (ii) the spectra of NaCl solutions are similar to that of pure water, (iii) the spectral intensities of NaI solutions are much larger than that of pure water in the 3300-3800 cm-1 region. The remarkable enhancement in the sps intensity for the NaI solutions is in contrast to the modest enhancement in the ssp intensity discussed in section 3. (To our knowledge, the salt concentration dependence on sps SFG spectra has not been reported experimentally. One would expect that the spectrum of 1.1 M NaI solution should show behavior intermediate between that of pure water and that of 2.1 M NaI solution.) We note here that the nonresonant amplitude, χNR izi , in eq 3 is empirically estimated from the experiments, as discussed below. Then, an important question arises of how the above features in the sps spectra, which appear quite different from ssp, can be understood in connection to the interface structure. Nonlinear Susceptibility. To address this question, we investigate the nonlinear susceptibility for the sps configuration as follows. Figures 8 and 9 show the real and imaginary parts of the resonant terms, χRizi, for NaCl and NaI solutions, where the nonresonant terms, -χNR izi , are represented with the horizontal dashed lines. We note that the nonresonant amplitude,
744 J. Phys. Chem. C, Vol. 111, No. 2, 2007
Ishiyama and Morita
Figure 5. Decomposed amplitude of the imaginary part of χRiiz by eq 10 for NaCl and NaI solutions. The definitions of the four components are given in eq 14.
Figure 7. Calculated sps polarized SFG spectra, ISFG sps , of pure water and NaCl and NaI aqueous solutions.
Figure 6. Schematic of the dipole-dipole correlation for (a) the z component and (b) the x component at the interface. An induced dipole of a molecule at the interface (green) couples with in-phase (blue) and out-of-phase (red) dipoles in the surrounding region.
χNR izi , strongly influences the spectral shapes in Figure 7 and that χNR izi should be negative and slightly dependent on the NaI concentration to describe the experimental sps spectra in the low-frequency tail region at about 3200 cm-1. Comparing the relative amplitude of the nonresonant to resonant terms, |χNR|/ |χR|, in the sps case (Figures 8 and 9) with ssp (Figures 3 and
4), it is apparent that the sps case has a relatively larger nonresonant amplitude than the ssp case over the entire frequency range in question. The larger background of sps is presumably attributed to the bulk contribution more emphasized in the sps configuration.45 Regarding the vibrationally resonant terms, χRizi, in Figures 8 and 9, all of the spectra of χRizi phenomenologically consist of three main spectral components, centered at ∼3400, ∼3550, and ∼3700 cm-1, where the second component has the opposite phase. The observed sps spectra in these aqueous systems could be reasonably represented by the three components along with the nonresonant background. While the second component is not clear in the calculated sps intensity in Figure 7 due to the interference with other components, it is discernible in the experimental sps spectra of pure water.10,46 Figure 8 shows that the dissolution of NaCl has little influence on the spectral shape of χRizi, whereas Figure 9 shows that the effect of NaI is remarkable, particularly in the striking enhancement in the spectral component at ∼3400 cm-1. The mechanism of the enhancement will be further discussed later in this section.
Analysis of Vibrational SFG Spectra
J. Phys. Chem. C, Vol. 111, No. 2, 2007 745
Figure 8. (a) Real and (b) imaginary parts of the izi (i ) x, y) nonlinear susceptibility, χRizi, for NaCl solutions and pure water. The insets show the self part, χRizi(self), in the same scale (see eq 8a). The dashed horizontal line in panel a indicates the level of -χNR izi .
Figure 9. (a) Real and (b) imaginary parts of χRizi for NaI solutions and water. The insets show the self part, χRizi(self). The dashed horizontal lines in panel a indicate -χNR izi levels for the systems of respective colors.
We also make a supplementary comment in Figures 8 and 9 about the apparently better signal-to-noise ratio in the calculated χRizi than the ssp counterparts in Figures 3 and 4, though the numbers of statistical sampling are common. The smaller noise from the bulk in the sps calculations is understood from the fact that both the macroscopic components of Axz (Ayz) and Mx (My) should vanish in the isotropic bulk in the sps calculations. In the ssp case, however, a macroscopic nonzero component of Axx (Ayy) remains even in the isotropic bulk, which hinders the convergence of χRiiz. Decomposition Analyses. The mechanisms of the nonlinear susceptibility, χRizi, are analyzed using the two decomposition schemes described in section 2.2, with particular focus on the contrasting aspects of sps spectra with ssp spectra. The first decomposition of χRizi is performed by eq 7 into self- and intermolecular correlations, χRizi(self) and χRizi(corr), and the results of the self part are displayed in the insets of Figures 8 and 9. By comparing χRizi(self) in the inset with χRizi in each panel, the most noticeable feature is that the amplitudes of χRizi are apparently larger than those of χRizi(self) particularly in the frequency region 3000-3600 cm-1. This feature is qualitatively different from the ssp case of χRiiz in Figures 3 and 4, where χRiiz is smaller than the self part due to the canceling mechanism of the intermolecular correlation part. The origin of the intermolecular correlation for the sps configuration is further discussed using the second decomposition scheme into molecular species by eq 10. Figure 10 displays R,IW the four components of χRizi in eq 14, that is, χR,WW , χR,WI izi izi , χizi , R,II and χizi , for NaCl and NaI solutions of 1.1 and 2.1 M
(green concentrations. For all of the panels in Figure 10, χR,IW izi lines) and χR,II izi (yellow lines) are negligibly small in compari(blue lines) and χR,WI (red lines), which is a son with χR,WW izi izi common feature to the ssp case in Figure 5. Comparing χR,WI izi (red lines) and χR,WW (blue lines), however, χR,WI is minor in izi izi all of the NaCl and NaI solutions, indicating that the amplitudes for χRizi mostly originate from the correlation of water polarizability and water dipole. The above feature is in contrast to the ssp case (see Figure 5) where the χR,WI term significantly iiz amplitude. In summary of the decomposicancels the χR,WW iiz tion analyses in the sps case, the nonlinear susceptibility, χRizi, is dominated by the correlation between water polarizability, W AW iz , and water dipole, Mi , with minor contribution of the ion components. These qualitative differences in the sps and ssp cases can be explained from the direction of the dipolar correlation at the gas-liquid interface. As illustrated in Figure 6, the dipoledipole coupling along the lateral (i()x,y)) direction of surface species is in phase (panel b) and accordingly cooperative, whereas the coupling along the vertical (z) direction is out of phase (panel a) and destructive. Consequently, the sps configuration relevant to the Mi component can involve larger constructive contribution of the intermolecular correlation effect than ssp to the Mz component. In the second decomposition, on the other hand, the ion dipoles in χR,WI have a more important role in the ssp configuration. This is essentially because ions have significant induced dipoles along the z direction at the interface (see section 4.3 of the preceding paper25), though they have no permanent dipole. The dipole moments of ions
746 J. Phys. Chem. C, Vol. 111, No. 2, 2007
Ishiyama and Morita
Figure 10. Decomposed amplitude of the imaginary part of χRizi by eq 10 for NaCl and NaI solutions. The definitions of the four components are given in eq 14.
accordingly have a larger contribution to the Mz component relevant to ssp than Mi to sps. Spatial Origin of Signals. A remaining issue to be addressed is to elucidate the strong enhancement of the sps component at about 3400 cm-1 in the NaI solutions. In order to help identify the spatial origin of this enhancement, we make use of the filtering function in eq 12 in section 2.3, which restricts the calculation of χR in the spatial region of zˆ > zˆr. By systematically changing the cutoff threshold, zˆr, from 0 to -7 Å, we observed . The results of Figure 11b the convergence behavior of χR,WW izi show that the enhanced signal of the NaI solution clearly comes from the region of -7 Å j zˆ j -3 Å, which coincides with the electric double layer region, as shown in panel a (see also Figures 6 and 8 of the preceding paper25). The dramatic enhancement of the sps signal reflects the electric double layer structure more sensitively than the ssp signal, since χizi is enhanced by the constructive intermolecular correlation. We also notice in Figure 11 that another small negative component at ∼3550 cm-1 observed for water and NaCl solution is attributed to the shallow region, -4 Å j zˆ. This implies that this spectral component is more sensitive to the topmost layer. The information obtained above will be used to assign the sps spectral components. Relation to Orientational Structure. On the basis of the above sps analyses, we discuss the assignment of the sps spectral components in terms of the orientational structure of the surface water. In the sps configuration, the correlation between the Aiz and Mi terms determines the sign and amplitude of the sps susceptibility, whereas each component vanishes on macroscopic average, that is, 〈Mi〉 ) 0 and 〈Aiz〉 ) 0. The broken symmetry at the interface along the z axis, an essential requisite for the SFG signal, is carried by the Aiz term in the sps configuration. On the other hand, the lateral projection of the molecular dipole moments tends to be in phase in a local region, as we have illustrated in Figure 6b, which makes a constructive contribution to Mi and enhances the amplitude. We note that a qualitative relation between the sign of Im[χR,WW ] and the average water orientation is observed in the izi sps susceptibility. This is originated from the fact that both the transition polarizability and dipole of Aiz and Mi associated with a local O-H stretching vibration of water molecules are roughly
directed along the O-H bond. Consequently, the sign of ] is qualitatively governed by the orientation of the Im[χR,WW iiz O-H bonds with respect to the z direction. This tendency in the sps case appears to be analogous to that in ssp, though the sign of the imaginary susceptibility is essentially determined by the Aiz term in sps, while by the Mz term in ssp, via the broken symmetry along the z axis. From Figures 8 and 9 and their insets, the sps susceptibility consists of three main components, centered at ∼3400, ∼3550, and ∼3700 cm-1, where the second component has the opposite phase. The components of 3700 and 3400 cm-1 with positive ] are attributed to water molecules with amplitudes in Im[χR,WW izi O-H bonds positively orienting in the zˆ direction. These components are arguably assigned as the water molecules of the dangling OH and the hydrogen bonding OH moieties, respectively. The dangling OH moieties at the gas-liquid interface should be oriented to the vapor side, though the calculated amplitude in the sps configuration is much less pronounced than that in ssp. It is also understandable that the imaginary part of χR,WW at 3400 cm-1 is positively emphasized izi by the induced orientational structure of water between the electric double layers, with the O-H bonds pointing to the vapor side as demonstrated in the preceding paper.25 On the other hand, the component of 3550 cm-1 with a negative amplitude in Im[χizi], which is observed in pure water and NaCl solutions, is attributed to water molecules near the Gibbs dividing surface, as discussed in Figure 11, with OH moieties pointing to the bulk liquid side, which qualitatively agrees with the spectrum assignment by Gan et al.10 We note that this configuration has been pointed out in Figure 8 of the preceding paper25 and assigned as the b state in Figure 10.25 5. Conclusions We have analyzed the SFG spectra of NaCl and NaI aqueous solutions with ssp and sps polarizations by molecular dynamics simulations. The MD calculations were performed using the flexible and polarizable water model that we have developed in the preceding paper. In the following, we summarize the main findings obtained through the present theoretical analyses. ssp Case. (i) In the ssp polarized SFG spectra, NaCl solutions show quite analogous spectra to those of pure water, while NaI
Analysis of Vibrational SFG Spectra
J. Phys. Chem. C, Vol. 111, No. 2, 2007 747 (v) The nonlinear susceptibilities for the sps spectra are enhanced by the intermolecular correlation part, particularly the correlation between water polarizability and water dipole. These mechanisms are in contrast to the ssp case. (vi) The susceptibilities for sps consist of three main spectral components, centered at about 3400, 3550, and 3700 cm-1, with the second component having the opposite phase. The first component is attributed to the hydrogen bonding water, and is sensitively enhanced by the double layer formation. The second component is assigned as the water near the topmost layer with OH bonds pointing to the bulk. The third component is assigned as the dangling OH bonds. Thus, we can conclude that the considerable enhancement in sps spectra of NaI cases is attributed to the constructive nature of the lateral intermolecular correlation in addition to the ordered orientation of water molecules in the electric double layer. As mentioned above, our simulations have revealed that the intermolecular correlation contribution plays essential roles in quantitative SFG analysis of the electrolyte aqueous solutions. These results suggest the need for an advanced analysis beyond the empirical interpretation of the nonlinear susceptibility as the sum of individual molecular hyperpolarizability contributions. The mechanisms of SFG spectra should be understood by explicitly taking account of molecular interactions, particularly in the case of liquid interfaces of strongly interacting molecules. We hope that the understanding of liquid interfaces will be advanced by elaborating the SFG analysis with the help of MD simulation, in order to fully exert the potential of the SFG spectroscopy. Acknowledgment. The authors would like to thank Dr. T. L. Tarbuck and Prof. G. L. Richmond for showing us the experimental sps spectra and Prof. Y. R. Shen for useful comments. This work was supported by the Next Generation Super Computing Project, Nanoscience Program, MEXT, Japan. References and Notes
Figure 11. (b) Imaginary part of χRizi for the region zˆ > zˆr. The bottom panel shows the converged result at zˆr ) -10 Å. In the upper panel (a), the density profiles of 2.1 M NaCl and NaI solutions are shown.25
solutions show modest enhancement at about 3400 cm-1. These features are consistent with the experiments. (ii) The nonlinear susceptibility, χR, is decomposed into the self-correlation, χR(self), and intermolecular correlation, χR(corr). In the ssp case, these two factors contribute in the same order and tend to cancel. The intermolecular correlation part could distort the intuitive relation between the nonlinear susceptibility and the molecular orientation, though the phase of the selfcorrelation part straightforwardly reflects the change of molecular orientation. (iii) The significant intermolecular correlation is qualitatively understood by the anisotropy of the dipole-dipole interaction at the surface, which induces out-of-phase vibrational coupling of water dipoles and ion dipoles along the surface normal. This mechanism, typically seen in NaI solutions, makes the ssp spectra less sensitive to the induced orientational structure by the electric double layer. sps Case. (iv) In the sps spectra, remarkable enhancement in the 3400-3800 cm-1 region is calculated for NaI solutions, while the spectra of NaCl solutions quite resemble that of pure water.
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