Chinese Chemical Letters

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1 Chinese Chemical Letters 26 (215) Contents lists available at ScienceDirect Chinese Chemical Letters journal homepage: Original article Role of refractive index in sum frequency generation intensity of salt solution interfaces Xia Li a, Rong-Juan Feng a, Ji-Jin Wang b, Zhen Zhang a, Zhou Lu a, *, Yuan Guo a, * a Beijing National Laboratory for Molecular Sciences, State Key Laboratory of Molecular Reaction Dynamics, Institute of Chemistry, Chinese Academy of Sciences, Beijing 119, China b School of Nuclear Science and Technology, Lanzhou University, Lanzhou 73, China ARTICLE INFO ABSTRACT Article history: Received 25 September 215 Received in revised form 2 October 215 Accepted 23 October 215 Available online 3 October 215 Keywords: Sum frequency generation Refractive index Interface Aqueous salt solution Sum frequency generation spectroscopy (SFG) has been widely used to study the interfacial chemistry of aqueous salt solutions of biological or environmental importance. Most of the SFG data analysis used the same bulk refractive index for different salt concentrations despite of the variations of the refractive indices. Here we systematically investigate the influence of the refractive index on the SFG intensities at various experimental conditions. It is discovered that the SFG intensities are the most sensitive to the refractive index at solid/liquid interfaces nearby the total internal reflection geometries. At air/liquid interfaces, the effect of the refractive indices is also nonegligible. Consequently some important SFG results, such as the response of water structures to the ionic strength at the SiO 2 /aqueous interfaces, are necessary to be reevaluated. These conclusions on the effect of the small variations of the refractive index are generally useful for the common practice of SFG data analysis. ß 215 Chinese Chemical Society and Institute of Materia Medica, Chinese Academy of Medical Sciences. Published by Elsevier B.V. All rights reserved. 1. Introduction 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 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 1,12,13], 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 * Corresponding authors. addresses: zhoulu@iccas.ac.cn (Z. Lu), guoyuan@iccas.ac.cn (Y. Guo). 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. 2. Theoretical background In a SFG-VS process, an infrared (IR) photon with the frequency of v IR is upconverted by a visible photon with the frequency of v vis, resulting in the emission of a new photon with the sum frequency v SF = v IR + v vis. The SFG intensity is proportional to the square of /ß 215 Chinese Chemical Society and Institute of Materia Medica, Chinese Academy of Medical Sciences. Published by Elsevier B.V. All rights reserved.

2 X. Li et al. / Chinese Chemical Letters 26 (215) the effective second order susceptibility I eff SF /j eff j2 [5,11,16], while for an achiral and rotationally isotropic eff interface can be expressed by the macroscopic susceptibilities (i=x, y, z) through [5,16]: eff;ssp ¼ L yyðv SF ÞL yy ðv vis ÞL zz ðv IR Þsinb IR yyz ¼ Fssp yyz yyz eff;sps ¼ L yyðv SF ÞL zz ðv vis ÞL yy ðv IR Þsinb vis yzy ¼ Fsps yzy yzy eff;pss ¼ L zzðv SF ÞL yy ðv vis ÞL yy ðv IR Þsinb SF zyy ¼ Fpss zyy zyy eff;ppp ¼ L xxðv SF L xx ðv SF þl zz ðv SF þl zz ðv SF ÞL zz ðv vis ÞL xx ðv vis ÞL zz ðv vis ÞL xx ðv vis ÞL zz ðv IR Þcosb SF cosb vis sinb IR ÞL xx ðv IR Þcosb SF sinb vis cosb IR ÞL xx ðv IR Þsinb SF cosb vis cosb IR ÞL zz ðv IR Þsinb SF sinb vis sinb IR ¼ Fpppx ð2þ þ Fpppx xz þ Fpppx zx þ Fpppx ð2þ where the indices of ssp, sps, pss and ppp are defined by the polarizations in the order of the SFG, visible and IR beams; b i is the incident angle against the surface normal. The L ii (i=x, y, z) terms are the Fresnel factors for the local field corrections, which can be calculated with the knowledge of b i and refractive indices n 1, n 2 and n. Namely, n 1, n 2 and n[3_td$dif] are for media 1 (the air or solids through which incident and SFG photons propagate), media 2 (the liquid phase), and the interfacial layer, respectively. The n[3_td$dif] values were estimated by the modified Lorentz model [16]. Here we only consider the common experimental arrangements with the copropagating laser configurations and the collection of the reflected SFG signals. For the ease of discussions, we define a coefficient F [4_TD$DIF] [2_TD$DIF] to represent the product of all the Fresnel factors L ii as well as the sines and cosines in front of the (i, j, k = x, y, z) term (Eq. (1)). The F [4_TD$DIF] coefficient carries all the information of the refractive indices, laser incident angles and polarizations. On the other hand, the molecular information is imbedded in the (1) term, which is determined by the microscopic hyperpolarizability tensors and average tilting angles of the interfacial molecules and has nothing to do with the refractive indices [5,11,16]. 3. Results and discussion As shown in Eq. (1), the contributions from the refractive indices are all contained in the F [4_TD$DIF]coefficients and readily to be [(Fig._1)TD$FIG] separated from the terms. Therefore, to find out whether it is necessary to correct the SFG intensity (I SF ) when the refractive indices change with the salt concentrations, one only needs to look into the dependence of F [4_TD$DIF]on n 2. In this context, we simulated F [4_TD$DIF] for both the typical air/liquid and solid/liquid interfaces. We used 5 mol/l NaCl solution as the model system of the salt solutions and compared the simulated F [4_TD$DIF] values (represented by F [4_TD$DIF] (NaCl)) with those for the pure water (represented by F [4_TD$DIF](H 2 O)). 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 3 and 38 cm 1 [2,3,6 1,12 15,18]. Thus during the simulations we first chose the IR wavelength to be 34 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 [4_TD$DIF]is a complex number. For the ssp, sps and pss polarizations, only one term is involved (Eq. (1)) [5,16]. Consequently the absolute values jf yyz j are sufficient enough to evaluate the changes of j eff j as a function of n 2 in the ssp, sps and pss spectra. For the ppp polarization, the spectral shape is determined by the interference of four terms (Eq. (1)) [5]. Therefore the phase term in each of the four F [4_TD$DIF]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 jf j for each of the four terms in the ppp polarizations. We first considered the air/liquid interfaces. Fig. 1a and b illustrate the simulated jf ðh 2 OÞj and jf ðnaclþjfor the air/liquid interface as a function of the visible incident angle b vis. During the simulation, the IR incident angle b IR was fixed to 588, which is in the range of the commonly used b IR values. The F yyz [5_TD$DIF] and F yzy [6_TD$DIF] in Fig. 1a correspond to the ssp and sps polarizations, respectively, while the F [7_TD$DIF], F [8_TD$DIF], F [9_TD$DIF] and F [1_TD$DIF] in Fig. 1b are for the four independent terms in the ppp polarization. The pss polarization yields similar spectra as sps, therefore will not be discussed. The change of n 2 caused by the increasing salt concentrations indeed plays an important role in the observed I SF. Fig. 1a and b shows that jf ðh 2 OÞj is always larger than jf ðnaclþj at the SiO 2 / Liquid Air / Liquid (a) F H 2 O NaCl (b) F yyz yyz yzy yzy H 2 O NaCl F (NaCl) / F (H 2 O) (d) F (e) F F (NaCl) / F (H 2 O) yyz yzy (c) (f) Fig. 1. The left and middle columns: jf j as a function of b vis 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: jf ðnaclþj=jf ðh 2 OÞj ratios vs. b vis at (c) the air/liquid and (f) fused silica/liquid interfaces.

3 1544 X. Li et al. / Chinese Chemical Letters 26 (215) air/liquid interface, indicating that jf j decreases when the salt concentration and n 2 increase. To better illustrate this difference between the salty and unsalted solutions, the ratios of jf ðnaclþj=jf ðh 2 OÞj were plotted as a function of b vis in Fig. 1c. It can be seen that the influence of the n 2 on the ssp and sps intensities is more evident at the larger visible incident angle because jf ðnaclþj=jf ðh 2 OÞj decreases with the increasing b vis for these two polarizations. At especially large b vis closes to the grazing angle, the jf ðnaclþj=jf ðh 2 OÞj 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 b vis between 358 and 658 [5]. According to Fig. 1c, typically a 1% drop in jfssp yyz j is anticipated under these conditions when the liquid changes from the pure water to 5 mol/l NaCl solution. This means that j eff;ssp j is 1% smaller if one uses the same n 2 of the pure water for the 5 mol/l NaCl solution. In other words, yyz at the air/liquid interface could be underestimated by 1%, corresponding to a 2% drop in I SF because the observed I SF,ssp is proportional to the square of j j [5,11]. This difference is not as negligible as eff;ssp previously thought [13]. For sps, the influence of n 2 on jfsps yzy j is more significant than that of ssp. But in general, the jf j factors of ssp and sps have similar responses to the changing n 2. Thecaseofppp is more complicated. Fig. 1b and c shows that at the air/liquid interface, n 2 has a smaller influence on the four pppjf j values than those of the ssp and sps, because the jf ðnaclþj=jf ðh 2 OÞj ratios for the four ppp tensors are larger than those for the yyz and yzy tensors. When b vis increases, jf ðnaclþj=jf ðh 2 OÞj decreases for the tensor, increases for the tensor, and only slightly changes for the and tensors. Because the n 2 -response is different for the four F [4_TD$DIF] factors, the interference among the four terms changes with n 2, causing the possible variations of the ppp spectral shape. Nevertheless, it is known that the ppp intensity for the hydrogen bonded water molecules at the air/water interface is usually small and people have traditionally paid more attention to the ssp spectra. Thus the influence of n 2 on the ppp intensity and spectral shape may be more important on the solid/liquid interfaces as discussed below. Fig. 1d[1_TD$DIF] 1f shows the dependence of the jf ðh 2 OÞj, jf ðnaclþj, and the jf ðnaclþj=jf ðh 2 OÞj ratios on b vis for the fused silica (SiO 2 )/aqueous interface. The SiO 2 /aqueous interface has been extensively used as the model system to investigate the mineralwater interactions [3,15]. Because n 1 is greater than n 2 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 b IR and b 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 b IR to be away from the critical angle in order to minimize the IR dispersions [17]. Therefore during the simulations, we fixed the b 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 jf j is much larger than the other three jf j factors in ppp when b vis is close to the critical angles (Fig. 1e), indicating that is the dominant one among the four ppp terms near [12_TD$DIF]TIR. Second, jf j curves beyond the critical angle are no longer monotonic. Particularly, jf yyz j, jf yzy j, and jf j all decrease with the increasing b vis when b vis is larger than the critical angle. As a result, although most of the SFG-VS experiments on the solid/liquid interfaces attempted to utilize the signal enhancement at TIR [3,14,17], b vis is not recommended to be larger than the critical angle. As seen from Fig. 1d f, the change of n 2 has much more dramatic effect on the SFG-VS spectra for the solid/liquid interfaces compared with the air/liquid interfaces. In addition, the influence of n 2 increases rapidly when b vis approaches the critical angles, indicating the correction of I SF by n 2 is more necessary near TIR. In the ssp and sps polarizations, the jf ðnaclþj=jf ðh 2 OÞj ratios are always smaller than 1 and can be as low as 45% when b vis reaches the critical angles (Fig. 1f), showing a strong dependence of F [4_TD$DIF]on n 2. Because I SF is proportional to the square of j j,a45% drop in eff jf yyz j will cause a 8% reduction in I SF for the ssp polarization. In the case of the ppp polarization, the F [4_TD$DIF] terms at the SiO 2 /liquid interfaces are also more sensitive to n 2 than those at the air/liquid interfaces. The jf ðnaclþj=jf ðh 2 OÞj curves for the tensor are almost identical to those of the yyz tensor in the ssp polarization and of the yzy tensor in the sps polarization, also approaching 45% when b vis reaches the critical angles. On the contrary, jf ðnaclþj=jf ðh 2 OÞj ratios for the and tensors show completely different n 2 -dependence. With the small b vis, jf ðnaclþj is slightly smaller than jf ðh 2 OÞj for and, similar to the other F [4_TD$DIF]factors. But when b vis increases toward the critical angles, jf ðnaclþjfactors for and becomes evidently larger than jf ðh 2 OÞj. Fig. 1f shows the extremely strong dependence of jf j on n 2 at the solid/liquid interfaces. As a result, the correction of I SF is of vital importance at the SiO 2 /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 SiO 2 /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 n 2 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 n 2 at different ionic strength (open circles in Fig. 2). For the ease of the data treatment, during corrections we used the IR wavelength of 32 cm 1, nearby the most intense peak at the SiO 2 /aqueous interface. [(Fig._2)TD$FIG] Fig. 2. I SF vs. [NaCl] at the SiO 2 /aqueous interface. The solid squares represent the experimental data from Ref. [3] before the correction by n 2. The open circles represent the same data after the correction by n 2.

4 X. Li et al. / Chinese Chemical Letters 26 (215) It is known that at the charged surface such as the SiO 2 /salty solution interface, both x (2) and x (3) terms contribute to the observed SFG intensities. Therefore the dependence of the x (3) intensity on n 2 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 jf ðnaclþj=jf ðh 2 OÞj ratios for yyz and yyx are almost identical near TIR, indicating x (3) and x (2) have the same n 2 - 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 n 2, therefore only changes by a few percentages compared with the values calculated without considering the variation of n 2. 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 n 2 - 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 x (2) and x (3). The daunting difference was observed for the corrected I SF at [NaCl] >.1 mol/l. In Hore s original work, a plateau between.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 n 2, the plateau in region c no longer exists. Instead, the corrected I SF rises when [NaCl] increases from.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 SiO 2 /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] <.1 mol/l, the insignificant change of n 2 is not enough to cause any observable differences (regions a and b in Fig. 2). In summary, the correction of I SF by n 2 is absolutely necessary for the concentrated salt solutions and a new physical model is needed to explain the corrected SFG curves at the SiO 2 / aqueous interface. The ppp intensity as a function of n 2 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 SFG- VS 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 b 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 n 2. Though the four jf j terms have different n 2 -dependences, the change of jf j at the solid/liquid interfaces might be more dominant near TIR due to the especially large jf j values (Fig. 1e). Thus near [12_TD$DIF]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 n 2 is more similar to jf j than other three jf j terms. As discussed above, the same dependence of jf j on n 2 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 n 2, 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 n 2 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 n 2, one has to take cautions to compare the interfacial molecular orientations at different salt concentrations. The detailed role of n 2 played in the SFG orientational analysis, however, is beyond the scope of this article and will be presented in a separate paper. 4. Conclusion 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 n 2 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 n 2 than that at the air/liquid interface. In addition, the dependence of I SF on n 2 changes with the laser incident angles. At the air/liquid interface, I SF is more sensitive to the n 2 variation at the larger visible laser incident angles; while at the solid/liquid interface, the maximum n 2 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 n 2 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. Acknowledgment This work was financially supported by the National Natural Science Foundation of China (Nos , and ). Appendix A. 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