The interfacial chemistry of salt solutions plays important roles in numerous atmospheric,geochemical and biological processes. Simple inorganic ions can enhance the reactions of the gaseous molecules at the outmost layer of the aqueous salt particles ^[1], alter the electrostatic fields at the mineral surfaces ^{[2, 3]},and regulate the secondary structures of the proteins ^[4]. Among the variety of surface analysis tools,sum frequency generation vibrational spectroscopy (SFG-VS) has drawn particular attentions owing to its intrinsic surface selectivity ^{[3, 5, 6, 7, 8, 9, 10, 11]}. By comparing the SFG-VS spectra obtained before and after adding the salts,one can deduce the structures of the interfacial hydrogen bond network, the surface propensities of ions ^{[7, 8, 9, 10, 12, 13]},and the nature of the electrical double layers near the charged surfaces ^{[2, 3, 14, 15]}.

With the growing number of SFG-VS studies on the salt solution interfaces,the quantitative interpretation of the spectra has become increasingly important. In the SFG-VS data analysis,the refractive indices are crucial parameters determining the magnitude of the local electric fields at the interfaces in relation to the incident laser fields ^{[5, 16]}. Most previous SFG data treatments used a constant refractive index for different salt concentrations because the refractive indices only vary by a few percentages when salt concentration increases ^[13]. However,in a recent report comparing the water structures at different solid/aqueous interfaces,it was demonstrated that the local electric field correction can sometimes differ significantly even with a small change of bulk refractive indices ^[15].

It is therefore necessary to examine the potential influence of refractive indices on the SFG intensity measurements in order to reevaluate the accuracy of the quantitative results. By simulating the local field corrections,we aim to generalize the circumstances under which the small variations of the refractive index can cause the significant impact on SFG-VS intensities. Different experimental scenarios,including the types of bulk media,the laser incident angles and polarizations,were considered. The effect of the IR dispersions has been thoroughly discussed in literature and will not be covered in this work ^{[5, 13, 15, 17]}. The influence of refractive indices on the SFG-VS intensities as discussed here can be used as a rule of thumb for any other liquid mixtures of which the refractive index varies with the bulk concentrations.

In a SFG-VS process,an infrared (IR) photon with the frequency of ω_IR is upconverted by a visible photon with the frequency of ω_vis, resulting in the emission of a new photon with the sum frequency ω_SF = ω_IR + ω_vis. The SFG intensity is proportional to the square of the effective second order susceptibility ^{[5, 11, 16]},while χ_eff⁽²⁾ for an achiral and rotationally isotropic interface can be expressed by the macroscopic susceptibilities χ_ijk⁽²⁾ (i = x,y,z) through ^{[5, 16]}:

For the ease of discussions,we define a coefficient F^ijk to represent the product of all the Fresnel factors Lii as well as the sines and cosines in front of the χ_ijk⁽²⁾ (i,j,k = x,y,z) term (Eq. (1)). The F^ijk coefficient carries all the information of the refractive indices,laser incident angles and polarizations. On the other hand, the molecular information is imbedded in the χ_ijk⁽²⁾ term,which is determined by the microscopic hyperpolarizability tensors and average tilting angles of the interfacial molecules and has nothing to do with the refractive indices ^{[5, 11, 16]}.

As shown in Eq. (1),the contributions from the refractive indices are all contained in the F^ijk coefficients and readily to be separated from the χ_ijk⁽²⁾ terms. Therefore,to find out whether it is necessary to correct the SFG intensity (I_SF) when the refractive indices change with the salt concentrations,one only needs to look into the dependence of F^ijk on n₂. In this context,we simulated F^ijk for both the typical air/liquid and solid/liquid interfaces. We used 5 mol/L NaCl solution as the model system of the salt solutions and compared the simulated F^ijk values (represented by F^ijk (NaCl)) with those for the pure water (represented by F^ijk (H₂O)). Since the refractive indices for the 5 mol/L NaCl solution are among the typical values for the concentrated aqueous salt solutions,the results obtained here can generally be used for other similar solutions.

Most of the SFG-VS studies explored the O-H stretching vibrations between 3000 and 3800 cm^{-1 [2, 3, 6, 7, 8, 9, 10, 12, 13, 14, 15, 18]}. Thus during the simulations we first chose the IR wavelength to be 3400 cm^-1,which is at the center of this vibrational region and nearby a typical SFG peak often assigned to the ‘‘liquid-like’’ water molecules ^{[2, 7]}. The visible wavelength was chosen to be 532 nm,a commonly employed visible wavelength in the SFG experiments.

Since the IR refractive indices contain imaginary parts,F^ijk is a complex number. For the ssp,sps and pss polarizations,only one χ_ijk⁽²⁾ term is involved (Eq. (1)) ^{[5, 16]}. Consequently the absolute values |F^yyz| are sufficient enough to evaluate the changes of |χ _eff ⁽²⁾| as a function of n₂ in the ssp,sps and pss spectra. For the ppp polarization,the spectral shape is determined by the interference of four χ_ijk⁽²⁾ terms (Eq. (1)) ^[5]. Therefore the phase term in each of the four F^ijk factors plays a role in the ppp intensity and it is difficult to draw a general conclusion. But as discussed below,we still can obtain some qualitative predictions by simulating the individual |F^ijk| for each of the four χ_ijk⁽²⁾ terms in the ppp polarizations.

We first considered the air/liquid interfaces. Fig. 1a and b illustrate the simulated |F^ijk(H₂O)| and |F^ijk( NaCl)| for the air/liquid interface as a function of the visible incident angle β_vis. During the simulation,the IR incident angle β_IR was fixed to 588,which is in the range of the commonly used β_IR values. The Fyyz and Fyzy in Fig. 1a correspond to the ssp and sps polarizations,respectively, while the F^xxz,F^xzx,F^zxx and F^zzz in Fig. 1b are for the four independent χ_ijk⁽²⁾ termsinthe ppppolarization.The psspolarization yields similar spectra as sps,therefore will not be discussed.

Fig. 1

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Fig. 1. The left and middle columns: |Fijk| as a function of βvis at (a) and (b) the air/liquid interface; (d) and (e) the fused silica/liquid interface. The solid lines are for the pure water and the dotted lines are for the 5 mol/L NaCl solutions. The right columns: |Fijk(NaCl)|/|Fijk(H2O)| ratios vs. βvis at (c) the air/liquid and (f) fused silica/liquid interfaces.

The change of n₂ caused by the increasing salt concentrations indeed plays an important role in the observed I_SF. Fig. 1a and b shows that |F^ijk(H₂O)| is always larger than |F^ijk(NaCl)| at the air/liquid interface,indicating that |F^ijk| decreases when the salt concentration and n₂ increase. To better illustrate this difference between the salty and unsalted solutions,the ratios of |F^ijk(NaCl)| =|F^ijk(H₂O)| were plotted as a function of β_vis in Fig. 1c. It can be seen that the influence of the n₂ on the ssp and sps intensities is more evident at the larger visible incident angle because |F^ijk(NaCl)| =|F^ijk(H₂O)| decreases with the increasing β_vis for these two polarizations. At especially large β_vis closes to the grazing angle,the |F^ijk(NaCl)|/|F^ijk(H₂O)| ratios for ssp and sps can be as low as 85%. Most of the SFG-VS spectra at the air/aqueous interfaces were taken in the ssp polarization and with β_vis between 358 and 658 ^[5]. According to Fig. 1c,typically a ~10% drop in |F_ssp^yyz| is anticipated under these conditions when the liquid changes from the pure water to 5 mol/L NaCl solution. This means that |χ_eff,ssp⁽²⁾| is ~10% smaller if one uses the same n₂ of the pure water for the 5 mol/L NaCl solution. In other words,χ_yyz⁽²⁾ at the air/liquid interface could be underestimated by ~10%,corresponding to a ~20% drop in I_SF because the observed I_SF,ssp is proportional to the square of |χ_eff,ssp⁽²⁾| ^{[5, 11]}. This difference is not as negligible as previously thought ^[13]. For sps,the influence of n₂ on |F_sps^yzy| is more significant than that of ssp. But in general,the |F^ijk| factors of ssp and sps have similar responses to the changing n₂.

The case of ppp is more complicated. Fig. 1b and c shows that at the air/liquid interface,n₂ has a smaller influence on the four ppp|F^ijk| values than those of the ssp and sps,because the |F^ijk(NaCl)|/|F^ijk(H₂O)| ratios for the four ppp tensors are larger than those for the yyz and yzy tensors. When β_vis increases, |F^ijk(NaCl)|/|F^ijk(H₂O)| decreases for the zzz tensor,increases for the xxz tensor,and only slightly changes for the xzx and zxx tensors. Because the n₂-response is different for the four F^ijk factors,the interference among the four χ_ijk⁽²⁾ terms changes with n₂,causing the possible variations of the ppp spectral shape. Nevertheless,it is known that the ppp intensity for the hydrogen bonded water molecules at the air/water interface is usually small and people have traditionally paid more attention to the ssp spectra. Thus the influence of n₂ on the ppp intensity and spectral shape may be more important on the solid/liquid interfaces as discussed below.

Fig. 1d-1f shows the dependence of the |F^ijk(H₂O)|,|F^ijk(NaCl)| , and the |F^ijk(NaCl)|/|F^ijk(H₂O)| ratios on β_vis for the fused silica (SiO₂)/aqueous interface. The SiO2/aqueous interface has been extensively used as the model system to investigate the mineralwater interactions ^{[3, 15]}. Because n1 is greater than n₂ for the solid/aqueous interfaces,most of the Fresnel factors for the solid/ aqueous interfaces are larger than those of the air/aqueous interfaces,especially when β_IR and β_vis approach the critical angles of the total internal reflections (TIR). This results in a significant enhancement of the recorded I_SF. However,York et al. suggested the IR incident angle β_IR to be away from the critical angle in order to minimize the IR dispersions ^[17]. Therefore during the simulations,we fixed the β_IR at 588,a few degrees smaller than the critical angle.

A couple of the points shall be noted in Fig. 1d and e. First,the |F^zzz| is much larger than the other three |F^ijk| factors in ppp when β_vis is close to the critical angles (Fig. 1e),indicating that χ_zzz ⁽²⁾ is the dominant one among the four pppχ_ijk⁽²⁾ terms near TIR. Second,|F^ijk| curves beyond the critical angle are no longer monotonic. Particularly,|F^yyz|,|F^yzy|,and |F^zzz| all decrease with the increasing β_vis when β_vis is larger than the critical angle. As a result,although most of the SFG-VS experiments on the solid/liquid interfaces attempted to utilize the signal enhancement at TIR ^{[3, 14, 17]},β_vis is not recommended to be larger than the critical angle.

As seen from Fig. 1d-f,the change of n₂ has much more dramatic effect on the SFG-VS spectra for the solid/liquid interfaces compared with the air/liquid interfaces. In addition,the influence of n₂ increases rapidly when β_vis approaches the critical angles, indicating the correction of I_SF by n₂ is more necessary near TIR. In the ssp and sps polarizations,the |F^ijk(NaCl)|/|F^ijk(H₂O)| ratios are always smaller than 1 and can be as low as ~45% when β_vis reaches the critical angles (Fig. 1f),showing a strong dependence of F^ijk on n₂. Because I_SF is proportional to the square of |χ_eff ⁽²⁾|,a ~45% drop in jFyyzj will cause a ~80% reduction in I_SF for the ssp polarization. In the case of the ppp polarization,the F^ijk terms at the SiO2/liquid interfaces are also more sensitive to n₂ than those at the air/liquid interfaces. The |F^ijk(NaCl)|/|F^ijk(H₂O)| curves for the zzz tensor are almost identical to those of the yyz tensor in the ssp polarization and of the yzy tensor in the sps polarization,also approaching 45% when β_vis reaches the critical angles. On the contrary, |F^ijk(NaCl)| =|F^ijk(H₂O)| ratios for the xxz and zxx tensors show completely different n₂-dependence. With the small β_vis, |F^ijk(NaCl)| is slightly smaller than |F^ijk(H₂O)| for xxz and zxx, similar to the other F^ijk factors. But when β_vis increases toward the critical angles,|F^ijk(NaCl)| factors for xxz and zxx becomes evidently larger than |F^ijk(H₂O)|.

Fig. 1f shows the extremely strong dependence of |F^ijk| on n₂ at the solid/liquid interfaces. As a result,the correction of I_SF is of vital importance at the SiO₂/liquid interface,especially when we try to use I_SF to quantitatively evaluate the surface charge,the thickness of the interfacial layer,or the surface adsorption isotherm. Hore and coworkers recently showed the response of I_SF to the increasing [NaCl] at SiO₂/aqueous interface ^[3]. As shown in Fig. 2,four distinct [NaCl] regions were identified according to the ssp intensity for the O-H stretching vibrations. These four regions were attributed to the combining effects of the surface charges,the screening of the surface DC field by the vicinity counter ions,and the disruption of the hydrogen bond network by the salts. But the influence of the n₂ was not taken into account in Hore’s original work,raising the questions about the accuracy of the data. In Fig. 2, we reprocessed Hore’s data and corrected the I_SF values by considering the changes of n₂ at different ionic strength (open circles in Fig. 2). For the ease of the data treatment,during corrections we used the IR wavelength of 3200 cm^-1,nearby the most intense peak at the SiO₂/aqueous interface.

Fig. 2

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Fig. 2. ISF vs. [NaCl] at the SiO2/aqueous interface. The solid squares represent the experimental data from Ref. [3] before the correction by n2. The open circles represent the same data after the correction by n2.

It is known that at the charged surface such as the SiO2/salty solution interface,both χ⁽²⁾ andχ⁽³⁾ terms contribute to the observed SFG intensities. Therefore the dependence of the χ⁽³⁾ intensity on n₂ has also to be considered. For ssp,x(3) consists of two tensors,yyz and yyx. As illustrated by Fig. S1 in Supporting information,the |F^ijk(NaCl)|/|F^ijk(H₂O)| ratios for yyz and yyx are almost identical near TIR,indicatingχ⁽³⁾ andχ⁽²⁾ have the same n₂- dependence at the experimental condition used by Ref. ^[3]. Other factors to be considered for the solid/liquid include the Debye length and coherent length. The former is linearly proportional to n₂,therefore only changes by a few percentages compared with the values calculated without considering the variation of n₂. The coherent length changes more significantly,but is always ordersof-magnitude larger than the Debye length (a few nanometers) and the interfacial thickness within which the SFG signals actually respond (a few molecular layers) ^[19]. Consequently,the n₂- dependence of coherent length and Debye length do not affect the correction of I_SF as discussed here.

The correction of overall I_SF in Fig. 2 has thus included the contributions from both χ⁽²⁾ and χ⁽³⁾. The daunting difference was observed for the corrected I_SF at [NaCl] > 0.1 mol/L. In Hore’s original work,a plateau between 0.1 mol/L and 1 mol/L [NaCl] was assigned to the transition from the Gouy-Chapman model to the Stern model during which the surface potential remained unchanged ^[3]. But after the correction by n₂,the plateau in "region c" no longer exists. Instead,the corrected I_SF rises when [NaCl] increases from 0.1 mol/L to 1 mol/L (open circles in Fig. 2), implying a dramatically different mechanism in this region. This increasing I_SF in "region c" might be in coincidence with the recent ultrafast dynamics measurement at the same SiO₂/water interface in which a faster dynamics at higher [NaCl] was suggested to be related to the larger electrical field and consequently more ordered water structures as [NaCl] increases ^[19]. With [NaCl] > 1 mol/L ("region d"),the corrected I_SF rapidly drops,but is still much higher than the uncorrected values at the same [NaCl]. Thus in the "region d",the interruption of the water hydrogen bond network by the concentrated ions is probable to be less severe as the raw SFG data indicated. With [NaCl] < 0.1 mol/L,the insignificant change of n₂ is not enough to cause any observable differences (regions a and b in Fig. 2). In summary,the correction of I_SF by n₂ is absolutely necessary for the concentrated salt solutions and a new physical model is needed to explain the corrected SFG curves at the SiO₂/ aqueous interface.

The ppp intensity as a function of n₂ is also more important at the solid/liquid interfaces than the air/liquid interfaces. Although the ppp polarization has not been commonly employed in the SFGVS studies on the solid/aqueous salty solution interfaces,we found in our recent experiments that it is possible for the ppp spectra to have the comparable intensities as the ssp spectra when β_vis is close to the critical angles. As a result the ppp spectra can potentially be used together with the ssp spectra to understand the surface water structures at the solid/aqueous interfaces. In this context,it is also worthwhile to evaluate the dependence of the ppp spectral intensity on n₂. Though the four |F^ijk| terms have different n₂-dependences,the change of |^Fzzz| at the solid/liquid interfaces might be more dominant near TIR due to the especially large jFzzzj values (Fig. 1e). Thus near TIR geometry that has been commonly employed in the SFG-VS studies on the solid/liquid interfaces,we can qualitatively predict that the dependence of the ppp intensity on n₂ is more similar to jFzzzj than other three |F^ijk| terms.

As discussed above,the same dependence of |F^ijk| on n₂ at the air/liquid interface is less obvious than that at the solid/liquid interface. However,it is still sometimes necessary to correct the measured I_SF by n₂,especially when one plans to use I_SF to quantitatively obtain an accurate interfacial adsorption isotherm as a function of the salt concentrations ^[8]. Accordingly,the Gibbs adsorption free energy,which is usually obtained through the curve fitting of adsorption isotherms,is also possibly subject to the similar corrections.

Last but not the least,the change of n₂ can potentially affect the orientational analysis in the SFG studies. The tilting angles of the interfacial molecules are often calculated by comparing the ssp and ppp intensities for the same vibrational mode ^{[5, 18]}. Since I_SF at different polarizations responds differently to n₂,one has to take cautions to compare the interfacial molecular orientations at different salt concentrations. The detailed role of n₂ played in the SFG orientational analysis,however,is beyond the scope of this article and will be presented in a separate paper.

In summary,the simulation results demonstrate that the ssp and sps intensities for both the solid/liquid and air/liquid interfaces of concentrated salt solutions would be underestimated if one uses the same n₂ value for the salt solutions and the pure water. The ppp spectral shapes and intensities are also possible to change accordingly when the salt solution becomes highly concentrated. It was found that I_SF at the solid/liquid interface is much more sensitive to n₂ than that at the air/liquid interface. In addition,the dependence of I_SF on n₂ changes with the laser incident angles. At the air/liquid interface,I_SF is more sensitive to the n₂ variation at the larger visible laser incident angles; while at the solid/liquid interface,the maximum n₂ sensitivity of I_SF occurs near the critical angles for the total internal reflections. Some important SFG results on the concentrated salt solutions therefore need to be reevaluated. The simulations used here are readily to be extended to other liquid mixtures of which n₂ changes with the bulk concentrations. This study also provides an important example showing that we have to be extremely cautious when quantitatively interpreting the SFG-VS data.

This work was financially supported by the National Natural Science Foundation of China (Nos. 21227802,21303216 and 21473217).

Supplementary data associated with this article can be found,in the online version,at http://dx.doi.org/10.1016/j.cclet.2015.10.020.